Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on th...Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.展开更多
Consider the bivariate exponential distribution due to Marshall and Olkin[2], whose survival function is F(x, g) = exp[-λ1x-λ2y-λ12 max(x, y)] (x 0,y 0)with unknown Parameters λ1 > 0, λ2 > 0 and λ12 0.Base...Consider the bivariate exponential distribution due to Marshall and Olkin[2], whose survival function is F(x, g) = exp[-λ1x-λ2y-λ12 max(x, y)] (x 0,y 0)with unknown Parameters λ1 > 0, λ2 > 0 and λ12 0.Based on grouped data, a newestimator for λ1, λ2 and λ12 is derived and its asymptotic properties are discussed.Besides, some test procedures of equal marginals and independence are given. Asimulation result is given, too.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.10571070 and 11001097
文摘Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.
文摘Consider the bivariate exponential distribution due to Marshall and Olkin[2], whose survival function is F(x, g) = exp[-λ1x-λ2y-λ12 max(x, y)] (x 0,y 0)with unknown Parameters λ1 > 0, λ2 > 0 and λ12 0.Based on grouped data, a newestimator for λ1, λ2 and λ12 is derived and its asymptotic properties are discussed.Besides, some test procedures of equal marginals and independence are given. Asimulation result is given, too.
